Handwriting rather than signature.
It presents itself (placement and form) as the signature of the original(?) owner. I have books inscribed without signatures and they do not look like this. I would look to examine other signed volumes to see any patters of placement/form - hand aside, and also check the volume and printing etc. For the hand I would of course examine as many letters and signed books as possible from this period before the film, as she appears to have lost interest in signing after the film was released and eventually started declining doing so. Good luck in your search!
I believe this was a gift. I found the great grandson on Facebook through his great grandmothers obituary. In the obituary she was born in November 1936, so I assume it was gifted to her as an infant.